Question: Solve for $x$ and $y$ using elimination. ${-4x-y = -31}$ ${-5x-y = -38}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${4x+y = 31}$ $-5x-y = -38$ Add the top and bottom equations together. $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-4x-y = -31}\thinspace$ to find $y$ ${-4}{(7)}{ - y = -31}$ $-28-y = -31$ $-28{+28} - y = -31{+28}$ $-y = -3$ $\dfrac{-y}{{-1}} = \dfrac{-3}{{-1}}$ ${y = 3}$ You can also plug ${x = 7}$ into $\thinspace {-5x-y = -38}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ - y = -38}$ ${y = 3}$